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Progress in Mathematics

Hyperfunctions and Harmonic Analysis on Symmetric Spaces

Authors: Schlichtkrull, Henrik

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Softcover $69.95
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About this book

During the last ten years a powerful technique for the study of partial differential equations with regular singularities has developed using the theory of hyperfunctions. The technique has had several important applications in harmonic analysis for symmetric spaces.

This book gives an introductory exposition of the theory of hyperfunctions and regular singularities, and on this basis it treats two major applications to harmonic analysis. The first is to the proof of Helgason’s conjecture, due to Kashiwara et al., which represents eigenfunctions on Riemannian symmetric spaces as Poisson integrals of their hyperfunction boundary values.

A generalization of this result involving the full boundary of the space is also given. The second topic is the construction of discrete series for semisimple symmetric spaces, with an unpublished proof, due to Oshima, of a conjecture of Flensted-Jensen.

This first English introduction to hyperfunctions brings readers to the forefront of research in the theory of harmonic analysis on symmetric spaces. A substantial bibliography is also included. This volume is based on a paper which was awarded the 1983 University of Copenhagen Gold Medal Prize.

Table of contents (8 chapters)

  • Hyperfunctions and microlocal analysis — an introduction

    Schlichtkrull, Henrik

    Pages 1-33

  • Differential equations with regular singularities

    Schlichtkrull, Henrik

    Pages 34-53

  • Riemannian symmetric spaces and invariant differential operators — preliminaries

    Schlichtkrull, Henrik

    Pages 54-62

  • A compact imbedding

    Schlichtkrull, Henrik

    Pages 63-78

  • Boundary values and Poisson integral representations

    Schlichtkrull, Henrik

    Pages 79-96

Buy this book

eBook $54.99
price for USA in USD (gross)
  • ISBN 978-1-4612-5298-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $74.99
price for USA in USD
  • ISBN 978-0-8176-3215-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $69.95
price for USA in USD
  • ISBN 978-1-4612-9775-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Hyperfunctions and Harmonic Analysis on Symmetric Spaces
Authors
Series Title
Progress in Mathematics
Series Volume
49
Copyright
1984
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston, Inc.
eBook ISBN
978-1-4612-5298-6
DOI
10.1007/978-1-4612-5298-6
Hardcover ISBN
978-0-8176-3215-1
Softcover ISBN
978-1-4612-9775-8
Series ISSN
0743-1643
Edition Number
1
Number of Pages
XIV, 186
Topics